ET- Expanded Temperament..kinda long.

[Richard Brekne]

> Phil Bondi writes:
>
> << I realize this is not re-inventing the wheel, but to the aural tuners out
> there, do you expand your temperament and why.?.?
>
> Phil
>

In a word... yes. Actually you could argue that all temperaments are expanded
since even a 2:1 octave type is wide relative to an integer multiple of the
fundemental to the lower note of the octave. So you kind of have a hard time of
avoiding it.

We "expand" octaves (and thereby a temperament) because the dance of coincidents
(and probably non coincidents as well) create different effects dependant on how
the two sets relate to one another..., and to themselves as well I should think.
Also this is somewhat dependant on our personal tastes. Some like the sound /
(feel) of a 6:3 stretch in that area and will divide an octave to suit.. Others
may select a 4:2 and still others are looking for something slightly different
then a strictly coincident partial relationship (ie Virgils natural beat
philosophy... which may be closely related to a kind of string coupling effect).

I opt for this latter, and find that this results often in a slightly narrow
6:3.. but not always I suspect. It think actually it might sometime result in a
slightly wide 6:3, I should probably measuring each piano I tune so as to see
what comes up. Might be interesting enough....Anyways I then make the
temperament fit the resultant octave. Sometimes I find that I end up getting a
bit too active 4ths and 5ths and have to squeze in a bit... but not too often.

Then like many others I move outwards on both ends of the temperament octave in
double checking how each new note fits in with the temperamant, and adjusting
either as necessary to achieve basically a 3 octave temperament.  From then on
in its just running through the bass, and then the treble useing the different
tests to make sure I am in the ball park while looking for that "sweet spot"
(relative to octaves) for each new note.

The point is to achieve as apparently a seemless beat effect between as many
principal intervals as possible. On really nice instruments when I have managed
my very best right now... its very easy to "feel" like  a double octave with a
5th thrown in  (ie 1, 5, 8, 16) is clean as a whistle and beatless as can be.
This of course is an illusion... at least relative to the coincident partial
perspective... but thats the point. When that added top octave note (the triple
then) plings through like crystal yet doesnt scream at you... well... then
everything has come together just right.

--
Richard Brekne
RPT, N.P.T.F.
Bergen, Norway
mailto:rbrekne@broadpark.no